Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#14559005 | C2 | semidirect |
| 3. #23752325 | C2 | semidirect |
| 4. #23752323 | C2 | semidirect |
| 5. #23752319 | C2 | semidirect |
| 6. #23752315 | C2 | semidirect |
| 7. #23752310 | C2 | semidirect |
| 8. #23752247 | C2 | semidirect |
| 9. #23752207 | C2 | semidirect |
| 10. #97×D151 | C2 | semidirect |
| 11. #441×C151 | C2 | semidirect |
| 13. #18012762 | C4 | semidirect |
| 41. #14559005 | C2×C4 | semidirect |
| 49. #14558991 | C2×C4 | semidirect |
| 50. D1208 | C2×C4 | semidirect |
| 54. C8×D151 | C2×C4 | semidirect |
| 65. Q16×C151 | C2×C4 | semidirect |
| 114. C151 | #2943 | semidirect |
| 121. #441 | D151 | semidirect |
| 165. Q16 | C4×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012762 | 2 |
| C4×#14559005 | 2 |
| #23752325 | 2 |
| #23752323 | 2 |
| #23752319 | 2 |
| #23752315 | 2 |
| #23752310 | 2 |
| #23752247 | 2 |
| #23752207 | 2 |
| #97×D151 | 2 |
| #441×C151 | 2 |
| #2943 | 151 |